Finite element discretisations of large-scale time-harmonic wave problems typically lead
to ill-conditioned linear systems with a large number of unknowns. A promising class of methods to solve such huge systems in parallel, both in terms of convergence and computing time, is offered by domain decomposition methods (DDMs). These approaches rely on a partition of the computational domain into smaller
subdomains, leading to subproblems of smaller sizes which are manageable by direct solvers. A robust domain decomposition (DD) preconditioner for large-scale computations is given in [1]}.
However, improving the efficiency of such preconditioners continues to be a challenging issue.
Recent work has shown that transmission operators
based on perfectly matched layers (PMLs) are well-suited for two-dimensional configurations of the Helmholtz problem within non-overlapping DDMs [2]}. Further, PMLs have been used successfully as transmission conditions in DDMs applied to geophysical applications modelled by the Helmholtz equation [3]}.
